{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 傅里叶变换的基本性质\n",
    "\n",
    "总的来说，傅里叶变换有这样几个性质：\n",
    "+ 线性性质（Linearity）\n",
    "+ 平移性质（Shift）\n",
    "+ 对称性质（Symmetry）\n",
    "+ 卷积性质（Convolution）\n",
    "\n",
    "参考 [傅里叶变换-wikipedia](https://zh.wikipedia.org/wiki/%E5%82%85%E9%87%8C%E5%8F%B6%E5%8F%98%E6%8D%A2#%E7%BA%BF%E6%80%A7%E6%80%A7%E8%B4%A8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 线性性质\n",
    "\n",
    "线性性质：两个函数之和的傅里叶变换等于各自变换之和，反之亦然\n",
    "![linearity](imgs/Linearity.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.fftpack import fft\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def generate_complex_signal(num_sample, k0):\n",
    "    '''\n",
    "    generate a complex signal\n",
    "    \n",
    "    num_sample : 信号的个数，即公式中的N\n",
    "    k0 : 周期个数\n",
    "    \n",
    "    returns\n",
    "    x : 复正弦信号\n",
    "    '''\n",
    "    \n",
    "    n = np.arange(num_sample)\n",
    "    x = np.exp(1j*2*np.pi*k0*n/num_sample)\n",
    "    \n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "E:\\ProgramData\\Anaconda3\\envs\\dl\\lib\\site-packages\\numpy\\core\\numeric.py:531: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
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5wVzi/nOzZPslHglhOGncF8x+EWhnq9xAo93RwmUi3XOJe2PE/100xzmzd+4G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\nAAAAAAw5CjsAAAAAGHIUdgAAAAAw5P4/OHGRIA1c9/0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e666f9a438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_sample = 100\n",
    "k0 = 20\n",
    "x1 = generate_complex_signal(num_sample, k0)\n",
    "\n",
    "num_sample = 100\n",
    "k0 = 10\n",
    "x2 = generate_complex_signal(num_sample, k0)\n",
    "\n",
    "X1 = fft(x1);\n",
    "X2 = fft(x2);\n",
    "mX1 = np.abs(X1);\n",
    "mX2 = np.abs(X2);\n",
    "\n",
    "x12 = x1 + x2;  # adding two signal\n",
    "X12 = fft(x12);\n",
    "mX12 = np.abs(X12);\n",
    "\n",
    "\n",
    "# plot the results\n",
    "plt.figure(figsize=(15,6))\n",
    "\n",
    "plt.subplot(321)\n",
    "plt.plot(x1)\n",
    "plt.subplot(322)\n",
    "plt.plot(x2)\n",
    "\n",
    "plt.subplot(323)\n",
    "plt.plot(mX1)\n",
    "plt.subplot(324)\n",
    "plt.plot(mX2)\n",
    "\n",
    "plt.subplot(325)\n",
    "plt.plot(mX1 + mX2)\n",
    "plt.subplot(326)\n",
    "plt.plot(mX12)\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 平移性质\n",
    "在时域上对信号进行平移，那么等价于在频域的复平面上旋转一个角度\n",
    "\n",
    "相反的，频域的复平面上旋转一个角度，等价于时域上的平移\n",
    "\n",
    "可以证明平移只对DFT的相位有影响，并不会改变DFT的幅度\n",
    "\n",
    "![shift](imgs/Shift.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CYkOjG0/sbkVfjw97u7yoczIoiIiodOWyOlJa+/KklBgJRHJ76gaGApicU38P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\noiRPRERERERkCfn/AcUnGjwdZJDsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e6677dc240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = np.linspace(0, 1.0, 50)\n",
    "x1 = np.append(x1,0)\n",
    "x1 = np.append(x1,np.linspace(-1.0, 0, 50))\n",
    "\n",
    "shifted_x = np.roll(x1, 10) # shift signal\n",
    "\n",
    "X1 = fft(x1)\n",
    "shiftedX = fft(shifted_x)\n",
    "\n",
    "mX1 = np.abs(X1)\n",
    "pX1 = np.angle(X1)\n",
    "pX1 = np.unwrap(pX1)\n",
    "\n",
    "mshiftedX = np.abs(shiftedX)\n",
    "pshiftedX = np.angle(shiftedX)\n",
    "pshiftedX = np.unwrap(pshiftedX)\n",
    "\n",
    "# plot the results\n",
    "plt.figure(figsize=(15,6))\n",
    "\n",
    "plt.subplot(321)\n",
    "plt.plot(x1)\n",
    "plt.subplot(322)\n",
    "plt.plot(shifted_x)\n",
    "\n",
    "plt.subplot(323)\n",
    "plt.plot(mX1)\n",
    "plt.subplot(324)\n",
    "plt.plot(mshiftedX)\n",
    "\n",
    "plt.subplot(325)\n",
    "plt.plot(pX1)\n",
    "plt.subplot(326)\n",
    "plt.plot(pshiftedX)\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 对称性质\n",
    "\n",
    "当x是实数信号，其傅里叶变换为X，则有对称性质：\n",
    "+ $\\mathfrak{R}\\{X\\}$ 是偶对称 $\\mathfrak{Z}\\{X\\}$是奇对称\n",
    "+ $|X|$是偶对称，$<|X|$是奇对称\n",
    "\n",
    "当x是偶对称的实数信号，其傅里叶变换为X，则有对称性质：\n",
    "+ $\\mathfrak{R}\\{X\\}$是偶对称 $\\mathfrak{Z}\\{X\\}=0$\n",
    "+ $|X|$是偶对称，$<|X|=n\\pi$或者0\n",
    "\n",
    "$\\mathfrak{R}$表示取实部，$\\mathfrak{Z}$表示取虚部，$|X|$为幅度，$<|X|$表示相位\n",
    "\n",
    "（找不到合适的例子，就不写代码了，直接上课件中的图片）\n",
    "\n",
    "![symmetry](imgs/Symmetry.png)\n",
    "![symmetry2](imgs/Symmetry2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 卷积性质\n",
    "\n",
    "在时域上的卷积操作，可以转换为两个信号傅里叶变换后的点乘操作\n",
    "\n",
    "相反的，傅里叶变换后的点乘，在时域上表现为卷积\n",
    "\n",
    "![convolution](imgs/Convolution.png)\n",
    "\n",
    "![convolution2](imgs/Convolution2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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c92DD/CiR5vpwdSHnPTiXzcWVPHLFUO4a3xd3nE71Y43+4jGqvKqO659dwh9m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\n4P8DV5c9Wb3FVZoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e667574748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.signal import get_window\n",
    "\n",
    "x1 = get_window('hanning', 256)\n",
    "x2 = np.cos( np.linspace(0, 2*np.pi, 256) )\n",
    "conv_x = np.convolve(x1, x2, 'same')\n",
    "\n",
    "X1 = fft(x1)\n",
    "X2 = fft(x2)\n",
    "CX = fft(conv_x)\n",
    "\n",
    "plt.figure(figsize=(15,6))\n",
    "\n",
    "plt.subplot(321)\n",
    "plt.plot(x1)\n",
    "plt.subplot(322)\n",
    "plt.plot(x2)\n",
    "\n",
    "plt.subplot(323)\n",
    "plt.plot(np.abs(X1))\n",
    "plt.subplot(324)\n",
    "plt.plot(np.abs(X2))\n",
    "\n",
    "plt.subplot(325)\n",
    "plt.plot(np.abs(CX))\n",
    "plt.subplot(326)\n",
    "plt.plot(np.abs(X1*X2))\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
